293 citations · 677 across the 21 of their papers we have counts for
5 papers · 1 filter
Data Driven Governing Equations Approximation Using Deep Neural Networks
Tong Qin, Kailiang Wu, Dongbin Xiu
We present a numerical framework for approximating unknown governing equations using observation data and deep neural networks (DNN). In particular, we propose to use residual netw…
Numerical Aspects for Approximating Governing Equations Using Data
Kailiang Wu, Dongbin Xiu
We present effective numerical algorithms for locally recovering unknown governing differential equations from measurement data. We employ a set of standard basis functions, e.g.,…
An Explicit Neural Network Construction for Piecewise Constant Function Approximation
Kailiang Wu, Dongbin Xiu
We present an explicit construction for feedforward neural network (FNN), which provides a piecewise constant approximation for multivariate functions. The proposed FNN has two hid…
Reducing Parameter Space for Neural Network Training
Tong Qin, Ling Zhou, Dongbin Xiu
For neural networks (NNs) with rectified linear unit (ReLU) or binary activation functions, we show that their training can be accomplished in a reduced parameter space. Specifical…
Energy Conserving Galerkin Approximation of Two Dimensional Wave Equations with Random Coefficients
Ching-Shan Chou, Yukun Li, Dongbin Xiu
Wave propagation problems for heterogeneous media are known to have many applications in physics and engineering. Recently, there has been an increasing interest in stochastic effe…